272 



PRACTICAL MATHEMATICS 



This result can be obtained in quite a different manner. For 

 since the sag d is very small compared with the half-span I, the 



curve is one of very small slope, and -p is therefore very small 

 for any value of x between and I. 



Hence 



l + 



= 1 + - approximately 



Then 



s = 



; * 



= 2[# + 

 = 21 + 



12a 2 



and 



- 6Z 2 



144. Areas of Surfaces of Revolution. Let PQ be a small arc of 

 the curve of length 8s, and this may be approximately taken as 

 a small chord of length 8s. (Fig. 86.) 



OC 



The area described as this chord rotates about the axis of x 

 is the small part of a conical surface. This area can be taken as 

 the difference between the curved surfaces of the two cones, 

 one whose slant side is CQ and the radius of the base is 



